answer all questions with explanation

P" . A researcher routinely tests using a nominal P (type I error) = 0.05, rejecting Ho if the P- value 5 0.05. An exact test using test statistics T has null distribution as follows: P (T = 0) = 0.30, P (T = 1) = 0.62, and P (T = 2) = 0.08, where a greater T provides more evidence against the null. Using the usual P-value determine the actual P (type I error)? (2 points) Using the mid Pvalue determine the P (type I error)? (3 points) Find P (type I error) in a) and b) when P(T= 0) = 0.30, P (T: 1) = 0.66, and P (T: 2) = 0.04. Comment on the conservativeness or liberalness of the exact test using the ordinary P-Value and the mid P-Value (3 points) In part a), a randomized-decision test generates a uniform random variable U from [0,1] and rejects Ho if both T = 2 and U 5 5/8. Determine the actual P (type I error)? (2 points)